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Angular statistics of Lagrangian trajectories in turbulence
Wouter J T Bos1, Benjamin Kadoch2, Kai Schneider3
1LMFA, CNRS UMR 5509, Ecole Centrale de Lyon, Université de Lyon, Ecully, France.
Physical Review Letters
|June 13, 2015
Summary
The angle between particle movements in turbulent flows follows two power laws, revealing the complex, multi-scale nature of high-Reynolds number turbulence. This directional change is self-similar and predictable using a model based on Gaussian velocity and acceleration.
Area of Science:
- Fluid Dynamics
- Turbulence Physics
- Statistical Mechanics
Background:
- Turbulence is characterized by complex, multi-scale dynamics across various Reynolds numbers.
- Understanding particle dispersion is crucial for modeling turbulent transport phenomena.
Purpose of the Study:
- To analyze the angular change between successive particle displacement increments in isotropic turbulence.
- To identify scaling laws governing particle trajectory evolution.
- To develop a theoretical model for directional changes in turbulent flows.
Main Methods:
- Evaluation of the angle between subsequent particle displacement increments as a function of time lag.
- Analysis of the probability density function (PDF) of directional changes.
- Derivation of an analytical model based on assumptions of Gaussianity and independence.
Main Results:
- The evolution of the angle exhibits two distinct power laws.
- These power laws are indicative of the multiscale dynamics inherent in high-Reynolds number turbulence.
- The PDF of directional change demonstrates self-similarity.
Conclusions:
- The study reveals fundamental scaling behaviors in particle dynamics within turbulent flows.
- The findings provide insights into the statistical properties of Lagrangian trajectories.
- An analytically derived model accurately approximates the observed directional change, supporting key assumptions about velocity and acceleration.
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